Like in the stock market? Psychologically people are more likely to buy if the price is lesser (ex. a 3 to 1 split turns btc from $230 to $80), and there would be no affect in the current value.
Would we really need to do this? This is like fooling up the masses. It's not surprising that stock markets are doing this, they are experts in fooling the masses. I don't talk about the divisibility of Bitcoin of course, this is OK as long as we give it another name as above is already suggested.
No. Nothing wrong in doing that.
Already we have wallet service which shows bitcoins in bits.
Dogecoin is successful just because of it's number not value.
So, its time to have exchanges list bitcoins in bits price. If we start from current price converted to bits, we may end up in 1$ per one bit in short period of time. That's the beauty, OP says.
No cheating involved in this.